Methemoglobin formation in mutant hemoglobin α chains: electron transfer parameters and rates

Abstract

Hemoglobin-mediated transport of dioxygen (O₂) critically depends on the stability of the reduced (Fe²⁺) form of the heme cofactors. Some protein mutations stabilize the oxidized (Fe³⁺) state (methemoglobin, Hb M), causing methemoglobinemia, and can be lethal above 30%. The majority of the analyses of factors influencing Hb oxidation are retrospective and give insights only for inner-sphere mutations of heme (His58, His87). Herein, we report the first all-atom molecular dynamics simulations on both redox states and calculations of the Marcus electron transfer (ET) parameters for the α chain Hb oxidation and reduction rates for Hb M. The Hb wild-type (WT) and most of the studied α chain variants maintain globin structure except the Hb M Iwate (H87Y). The mutants forming Hb M tend to have lower redox potentials and thus stabilize the oxidized (Fe³⁺) state (in particular, the Hb Miyagi variant with K61E mutation). Solvent reorganization (λ_solv 73–96%) makes major contributions to reorganization free energy, whereas protein reorganization (λ_prot) accounts for 27–30% except for the Miyagi and J-Buda variants (λ_prot ∼4%). Analysis of heme-solvent H-bonding interactions among variants provide insights into the role of Lys61 residue in stabilizing the Fe²⁺ state. Semiclassical Marcus ET theory-based calculations predict experimental k_ET for the Cyt b5-Hb complex and provide insights into relative reduction rates for Hb M in Hb variants. Thus, our methodology provides a rationale for the effect of mutations on the structure, stability, and Hb oxidation reduction rates and has potential for identification of mutations that result in methemoglobinemia.

Significance

Hemoglobin function is dependent on the stability of the heme ferrous (Fe²⁺) state. Some mutants stabilize the ferric (Fe³⁺) state, leading to methemoglobin (Hb M) formation that can be fatal. Current literature provides only retrospective analysis for these findings. We utilized molecular dynamics simulations to calculate electron transfer (ET) parameters and provide biophysical insights into the mechanisms for Hb M formation and reduction. Furthermore, we modeled Hb-Cyt b5 complex dynamics and calculated ET parameters to estimate ET rates (k_ET) that agree closely with literature reports. Our methodology allows consistent prediction of ET parameters and reduction rates, which has potential use in the identification of mutations resulting in methemoglobinemia.

Introduction

Hemoglobin variants are widespread in the human population, as seen in the HbVar database (http://globin.cse.psu.edu/hbvar/menu.html). These variants lead to two broad classes of disorders: 1) globin synthesis and assembly disorders known as thalassemias and 2) globin structure disorders (methemoglobinemia, sickle cell anemia, and disorders caused by unstable and altered dioxygen (O₂) affinity Hb variants) (1). Hb variant characterization, biochemical properties, and associated clinical manifestations have been reviewed recently (2,3). Hb is normally present in the reduced (Fe²⁺, 99%) state and effectively transports O₂ between lungs and tissues. In red blood cells, the concentration of the oxidized Hb, methemoglobin (metHb, also known as Hb M), is kept below 1% by enzymatic (NADPH-dependent flavin reductase and cytochrome b5) and nonenzymatic (e.g., ascorbic acid) reductive pathways (4). Higher levels (∼10%) can lead to cyanosis and reduced O₂ delivery, and levels above 30% can be lethal. This condition, known as methemoglobinemia, can be induced by drugs (chloroquine/hydroxychloroquine), inherited defects in cytochrome b5 (or its reductase), or inheritance of an Hb variant characterized by an increase in the stability of oxidized (ferric, Fe³⁺) or a decrease in the stability of the (ferrous, Fe²⁺) states (5, 6, 7, 8, 9, 10). Methemoglobinemia has been reported in many coronavirus disease 2019 (COVID-19) patients (11, 12, 13), thus potentially complicating the assessment of blood O₂ saturation levels in respiratory distress. Incidence of COVID-19 in patients with sickle cell disease (characterized by Hb S) was found to be 85%, but the prevalence of other Hb variants in COVID-19 patients remains unexplored (14).

A large body of information and knowledge is available in the form of more than 1820 known variants, >600 human Hb structures in the Protein Data Bank, and a large number of biochemical, genetic, spectroelectrochemical, and modeling studies. The structure and function of Hb and impact of mutations on O₂ affinity has been reviewed in the past (15, 16, 17). The Hb globin structure has eight helices that maintain a hydrophobic environment around the heme and stabilize Fe²⁺ state to ensure reversible O₂ binding. Structural changes that destabilize the globin or expose heme to solvent enhance oxidation rates and Hb M formation. Robust clinical and biochemical tests (HPLC, electrophoretic, MALDI-TOF, and PCR), are available for the characterization of different variants, for example, sickle cell Hb (Hb S) and thalassemic forms (Hb F) (3), but functional characterization of these variants in terms of O₂ affinity or Hb M content, oxidation, and reduction rates is extremely rare (18).

Thus, the in vivo rates for Hb oxidation to Hb M and reduction of Hb M back to the Fe²⁺ state for many Hb variants remain unknown. These unknowns can potentially lead to failures in diagnosis, delays in the treatment, and overtreatment and even cause treatment failures with standard therapies such as methylene blue (9,19). Additionally, because of the lack of knowledge of factors like optimal reductant concentrations and O₂ pressures, Hb M content can go unrecognized and reach toxic levels, causing cyanosis and even fatality. Thus, reliable estimation of the relative Hb oxidation and Hb M reduction rates for different Hb variants is urgently required.

The experimental redox potentials (E°) for Hb and Hb subunits depend on the details of the experimental method (direct electrochemistry or spectroelectrochemistry), the nature of the electrodes and their interactions with Hb, and conditions, e.g., the presence of O₂, pH (Bohr effect), ionic strength, redox mediator, and temperature. Literature values range from −0.172 to +0.050 V. In studies with the Hb tetramer, the identity of the subunits undergoing the redox changes are uncertain. Earlier, Mateescu et al. have performed cyclic voltammetry experiments to determine the Hb E°-values under acidic and aerobic and neutral and anaerobic conditions, which are known to stabilize the T (tense) and R (relaxed) states, respectively (20). The authors assigned E°-values of −0.040 and −0.165 V, respectively, to the R and T states of Hb. Guiles et al., have measured the E° of Hb and Cyt b5 and used Marcus theory to predict reorganization energies (λ) and homogenous and heterogenous ET rates (21). Similar variations in the E°-values were observed in the presence and absence of O₂, which is characteristic of R and T states.

The Marcus theory of electron transfer (ET) and its variants have been successfully applied in the areas of material science, small molecule charge-transfer complexes, redox heme, and nonheme proteins involved in respiratory and mitochondrial ET chains (22). Because Hb is a tetramer with two identical α and β chains that contain identical Fe-porphyrin (heme) cofactor, experimental measurements of enzymatic and nonenzymatic Hb reduction rates for individual subunits and applications of ET theories have proved challenging. The generally accepted mechanism of Cyt b5 and Hb interaction is considered to involve an initial complex formation, followed by the ET between the two proteins (Eq. 1) (23,24). The observed rate constant, k_app, can be written as a product of the equilibrium constant of binding, k_b, and the rate constant for ET, k_ET, k_app = k_b × k_ET. McLendon et al. have used reconstituted [Zn, Fe] hybrid Hb dimers in which heme iron in one of the chains has been replaced with zinc (24). These hybrid Hbs show a larger free energy change (ΔG°) associated with the reduction (Eq. 1) compared with the Hb wild-type (WT). Because of the weaker interaction between Cyt b5 and Hb, these measurements were made at lower temperatures (∼10°C) and extrapolated to 25°C. Using Marcus theory and assuming a constant reorganization energy of (λ = 0.9 V), the authors calculated ET rates (k_ET) for the WT and hybrid Hb. The Hb WT k_ET = 1.6 s⁻¹ was estimated to be in close agreement with experimental values of 1 and 2 s⁻¹ at pH 7 and 6, respectively, at 10°C. Based on the binding constant (k_b) and observed k_app = 770 M⁻¹, the authors calculated k_ET = 120 s⁻¹ for the Hb WT at 25°C. ET rates from the photoinduced excited state of hybrid Hb were ∼1500-fold higher because of a larger driving force.

$$Cytb5\left(F{e}^{2+}\right)+HbM\left(F{e}^{3+}\right)\leftrightarrow Cytb5\left(F{e}^{2+}\right)\dots HbM\left(F{e}^{3+}\right)\to Cytb5\left(F{e}^{3+}\right)+Hb\left(F{e}^{2+}\right).$$ (1)

Earlier studies by Mauk et al. had found spectroscopic evidence for quantitative formation of 1:1 Cyt b5-Hb complexes (25). Extending this work, they proposed a model for the Cyt b5-Hb complex in which the heme edges are 8 Å apart and the Fe-Fe distance in the complex was 16 Å (26). Hb residues (Lys 54, 56, 60, 61, 90, heme propionates) and Cyt b5 residues (Glu 43, 44, 48, Asp 60, and heme propionates) were postulated to be involved in complex formation. Later, Hoffman et al. used similar Hb hybrids and determined the ET rates for individual Hb subunits (27). The α subunit showed fourfold higher binding affinity and twofold faster ET rates compared with the β subunits. These findings were similar to earlier reports of the ET between Hb and inorganic complexes (28). Brittan et al. performed Brownian dynamics and electrostatics calculations to reassess the structural requirements for efficient ET between Cyt b5 and embryonic Hb (29). Although there was a decent agreement with Mauk et al. (25) regarding the identity of residues involved in the complex formation, the ET rates were overestimated for the Hb WT and were similar to the hybrid Hb. None of these studies have performed all-atom molecular dynamics (MD) simulations of the redox states to estimate Marcus parameters and ET rates.

A combination of quantum chemical calculations and MD simulations has been used to estimate Marcus ET parameters (λ, ΔG°) and ET rates for other redox proteins (30, 31, 32, 33, 34, 35, 36, 37). These methods make use of the linear response approximation to estimate the free energy parabolas, which allows the estimation of λ and ΔG° from the thermal averages of the energy gaps (<ΔE>) for the oxidized (O) and reduced (R) states (32). ET rates can then be predicted using either the full estimation of electronic coupling matrix and Frank-Condon factors or using empirical parameters for protein packing density along with the Marcus parameters (38,39). Studies with other redox proteins have shown that mutations both within and outside the active sites lead to significant changes in the Marcus parameters that ultimately modulate the ET rates and protein functions (38, 39, 40, 41). MD simulations for the Hb WT have been reported earlier (42, 43, 44, 45, 46, 47, 48). These mostly focused on the allosteric mechanisms of ligand binding and T → R transitions. More recently, Case and Samuel have studied the dynamics of Hb M and associated heme loss (49). But the calculations or estimations of the Marcus parameters and ET rates for Hb WT and its variants using all-atom MD simulations have not been reported to date and represent gaps in our understanding of how globin mutations influence Hb oxidation and reduction and Hb M content via modulation of ET parameters. Reliable predictions of ET parameters for Hb WT and its variants can provide atomic-level and functional insights into factors influencing Hb oxidation. This information can prove valuable in identifying potential Hb variants with increased propensity for oxidation and Hb M formation. It may also prove useful in the design of novel alternative therapeutic interventions in populations in which classical therapy (e.g., methylene blue) is contraindicated. Indeed, the design of safer blood substitutes has been attempted, but clinical development has often been hampered by heme-oxidation-induced toxicity (50,51).

In this work, we performed all-atom MD simulations on the Hb WT and variant α Hb chains and of the WT α Hb-Cyt b5 complex for the estimation of the parameters that determine the thermodynamics and kinetics of Hb reduction, in particular heme redox potentials (E°), driving force (ΔG°), reorganization free energies (λ), electronic coupling (H_ab), ET activation free energies (ΔG^‡), and ET rates (k_ET). We address the following key questions with respect to Hb oxidation and Hb M reduction among selected Hb variants. 1) What is the influence of Hb M stabilizing α chain mutations on the globin structure and stability? 2) Can a protocol utilizing quantum chemically derived parameters and all-atom MD simulations be used to estimate ET parameters for the α Hb chain and its redox partner Cyt b5? 3) What is the influence of Hb M stabilizing mutations on the ET parameters and ET rates? 4) How do these mutations affect outer-sphere (including protein and solvent) reorganization energies (namely λ_os = λ_prot + λ_solv) and the ET driving force? 5) Do these thermodynamic and kinetic parameters provide insights into the Hb M reduction rates? 6) Can the ET parameters and rates provide insights into the relative Hb M reduction rates among Hb variants?

Materials and methods

Protein preparation

Hemoglobin (Hb) α chain coordinates were extracted from T-state structure PDB: 1HGA (A chain) (52,53). This structure represents the deoxy-Hb in the T state. As seen in Fig. 1, the alignment of the protein backbone of this structure with the oxidized methemoglobin (Hb M) PDB: 1HGB shows very similar structure (backbone and all-atom root mean squre deviation (RMSD) = 0.186 and 0.233 Å). Thus, the PDB: 1HGA structure was chosen for further analysis. The protonation states for the protein chain were estimated at pH 7.4 with H++ 3.0 (54) via its webserver (55). Total charge on the globin chain was +1 at this pH. For Cyt b5 modeling, the PDB: 3NER (56) structure was selected, and protein was prepared for MD simulations using a similar procedure. Total charge on the Cyt b5 structure was −11 at pH 7.4. A TIP3P water box of 10 Å was added around the proteins, followed by counterions (Na⁺ or Cl⁻) such that the proteins in the Fe²⁺ redox state are neutral, and thus, the Fe³⁺ states have +1 charge.

Figure 1.

Alignment of α chains of hemoglobin structures in the reduced (PDB: 1HGA, blue) and oxidized (PDB: 1HGB, light orange) states. The Fe-N (His87) distances in 1HGA and 1HGB are 2.214 and 2.153 Å, respectively. The corresponding Fe-N (His58) distances are 4.444 and 4.303 Å. These parameters are in agreement with the geometry of heme complexes, in which the Fe is displaced out of the plane of the porphyrin ring unless coordinated with additional axial ligands such as O₂ and the oxidized state is a low-spin hexacoordinate that usually interacts with water or with His58. Dashed light yellow lines indicate that residues interact with each other. Amino acids in red indicate mutation sites studied in this work. To see this figure in color, go online.

Heme parameterization with MCBP.py and quantum chemical calculations

Metal Center Bond Parameter python tool (MCBP.py) (57) available in AmberTools18 (58) was used for heme and axial ligand parameterization in both the redox states of Cyt b5, Hb, and Hb variants. A procedure similar to that described for the CYP450 BM3 (Amber advanced tutorial http://ambermd.org/tutorials/advanced/tutorial20/mcpbpy_heme.htm) was used (see Supporting materials and methods for details).

Equilibration and production simulations

A robust 10-step protocol recently reported by Roe and Brooks was used to equilibrate the structures of Hb α chains, its variants, Cyt b5, and the Cyt b5-Hb complex studied in this work (59). Briefly, step 1 involved minimization of solvent while keeping strong (5.0 kcal/mol Å) restraints on the protein, porphyrin ring, Fe, and the axial ligand. In step 2, a short 15 ps MD simulation with NVT, weak-coupling thermostat was performed while retaining the restraints. Step 3 was 1000 steps of minimization with weaker (2.0 kcal/mol Å) restraints on the same atom selection. Step 4 continued minimization for 1000 steps with even weaker (0.1 kcal/mol Å) restraints on the same atom selection. Step 5 was the final minimization for 1000 steps without any restraints. Step 6 was MD simulation for 5 ps, with moderate (1.0 kcal/mol Å) restraints on the same atom selection, using an NPT ensemble. Steps 7 and 8 were additional relaxation for 5 and 10 ps, respectively, with NPT and smaller (0.5 kcal/mol Å) restraints. Step 9 involved unrestrained relaxation for 10 ps. The final density equilibration was performed in 1 ns increments without any restraints under periodic boundary conditions, hydrogens were restrained with SHAKE on, a collision frequency was set to 5 ps⁻¹ as recommended for Langevin thermostat, and the temperature was set to 300 K. This protocol defines three parameter values as robust criteria for declaring the equilibration success. The criteria are 1) the value for the slope of the density versus time plot should be less than 10⁻⁶. 2) The final density of the system should not differ from the average of the second half of the density data by more than 0.02 g cm⁻³. 3) The fitted exponential χ² value should be less than 0.5. All the structures simulated in this work passed these criteria and thus were used for production runs and further analysis. This protocol, available via the AmberMDPrep shell script, requires the latest version of cpptraj (V4.30.2), which was installed from GitHub and sourced before running the protocol (60).

The structures for the Hb variants were prepared by renaming the chosen backbone residue names and deleting the side-chain atoms from the Protein Data Bank file. The mutant side-chain rotamers without clashes and highest probability were selected from the Dunbrack’s rotamer library available in Chimera (61,62). Identical protocols were used for equilibrating the Hb variant α chains in both redox (Fe²⁺ and Fe³⁺) states. The summary of mutation categories in the HbVar database contains information on 363 α chain variants. The summary table also gives 13 variants classified as methemoglobins, four of which are α chain variants. Nonetheless, many of the 363 α chain variants (not classified in the database as methemoglobins) do form Hb M. Thus, we additionally selected variants that have been characterized in the literature (63) and are known to form methemoglobin (Hb M) and/or lower the concentration of reduced Hb, namely Hb M Boston (H58Y), Hb M Iwate (H87Y), Hb Miyagi (K61E), and Hb Kirklareli (H58L). Additionally, a single point mutant for which Hb M formation has not been reported, Hb J-Buda (K61N), was studied.

Protein-protein docking between Cyt b5 and Hb using HADDOCK webserver

Protein-protein docking between Cyt b5 (PDB: 3NER) and Hb (PDB: 1HGA) WT α chain was performed using High Ambiguity Driven protein-protein DOCKing 2.2 (HADDOCK 2.2. webserver) (64). The interacting residues mentioned in the introduction were chosen to dock the two proteins with no additional restraints. HADDOCK found 162 structures, which were grouped into seven clusters. As seen in Table S1, cluster 3 contained nine structures that were found to have similar scores, suggesting similar binding. A closer inspection of these HADDOCK-predicted structures showed that the expected protein-protein and heme interactions were present in only the top-ranked structure (HADDOCK score = −37.4 ± 6.0 and z-score = −1.1; see Fig. 5). Furthermore, cluster 3 showed the most favorable van der Waals and electrostatic energies, and the desolvation energy was comparable with other clusters. This prediction, in which out of the many degenerate structures, only a small fraction are ET competent (i.e., close heme-heme and favorable protein-protein interactions), is in agreement with the “dynamic docking” hypothesis proposed earlier by Wheeler et al. for the Cyt b5-Hb complex (23). Thus, this structure was prepared for MD simulations using the protein preparation, heme parameterization, and equilibration protocol mentioned in Heme parameterization with MCBP.py and quantum chemical calculations and Equilibration and production simulations above.

Figure 5.

Shortest heme edge-to-edge and Fe-Fe distances (Å) in the Cyt b5-Hb complex. (A) shows these distances in the initial structure, and (B) shows the evolution of these distances during a 40 ns MD simulation. To see this figure in color, go online.

Results and discussion

Reduction of the monomeric α chain of Hb WT has been studied earlier (23,65). These studies found that the redox behavior of the α Hb chain in monomeric state is almost identical to the Hb tetramer. Thus, studying the redox properties of a single α Hb monomer as done here is justified and can be expected to meaningfully represent the redox and ET processes in the tetramer. As noted by Hub et al., most of the experimental studies monitor the hydrogen bond dynamics between a small set of selected interchain residues, e.g., αAsp94-βTrp37 and αTyr42-βAsp99 (44). These interactions are interpreted in terms of conformational transitions (T ↔ R) without further investigation. NMR studies in solution have identified that α chain His45, Tyr42, Thr41, His89, His50, and His72 residues play an important role in Bohr effect, whereas residues around Asp94 and His122 participate in α1β2 subunit interactions (17).

Influence of Hb α chain mutations on the structure and stability

Realizing the dynamical nature of Hb α chain interactions, the effect of Hb M stabilizing mutations on the dynamics and flexibility of various globin regions was investigated. Residue-wise backbone root mean-square fluctuations (RMSFs) on the equilibrated trajectories (40 ns) were calculated with cpptraj (as seen in Fig. 2). As expected, the N- and C-termini show higher fluctuations. A comparison of the RMSFs for residues ∼10–130 shows that the overall globin structure is similar among variants, except Hb M Iwate, which involves mutation of the axial histidine ligand with tyrosine (H87Y). This mutation is known to destabilize the heme globin structure and function (66).

Figure 2.

RMSF for the protein backbone for the WT Hb, mutants leading to the formation of Hb M (Iwate and Boston variants), and H58R mutant, which is analogous to the β chain Hb Zurich variant. The RMSF was calculated for 2000 snapshots extracted from a 40 ns MD trajectory. To see this figure in color, go online.

To assess the influence of other mutations that show a stable globin structure but nonetheless oxidize to Hb M, the RMSF values among their redox states were compared. For this, a Student’s t-test matrix among all the variants was calculated (see Table S2). Residue-wise RMSFs are considered similar for pairs that show a p-value more than 0.05. Mutation of the distal histidine with tyrosine (H58Y) seen with the Boston Hb variant maintains the overall globin structure. The largest backbone fluctuations are in the residues 44–54, 89, 90, and 114–119 (see Fig. 2). The region 44–54 is a loop that has important hydrophobic (Phe43, 46-heme) and electrostatic (His45-heme carboxylate) interactions that stabilize the heme in the WT, whereas the region 114–119 has key interactions with the β chain residues (Arg30, and His116). The RMSF (excluding four terminal residues) for the redox state between WT and H58Y variant shows that fluctuations are significantly different and the average, minimum, maximum, and standard deviation are larger for the H58Y variant (Tables S2 and S3). This indicates that this mutation destabilizes both the redox states.

Mutation of the His58 to Arg, analogous to the H58R Zurich variant of the β chain, shows similarly large variations in these regions in addition to a larger fluctuation in the loop 117–120. These findings are consistent with the large size of the Arg side chain (similar to Tyr), which leads to similar motions of these regions as manifested by higher RMSF value (see Fig. 2). The fluctuations induced by H58R mutation are significantly different, and average values are about twice from the Hb WT (Tables S2 and S3).

A close inspection of the globin and heme structure in Hb M Iwate during the MD simulation shows that the heme group significantly moves out of the protein pocked and gets exposed to the solvent medium (see Fig. S1). It is known in the literature that the Hb M Iwate structure is not stable, and there is experimental evidence that the heme group gets transferred to the distal histidine in the reduced state (66). Considering the large structural changes that H87Y mutation induces in the Hb structure and the lack of crystal structure, we choose not to use these MD trajectories to investigate the effect on Marcus parameters, oxidation energies, and ET rates for this Hb variant.

The RMSF analysis for the Hb Miyagi and Kirklareli variants (K61E and H58L), which are known to form Hb M, showed similar RMSFs (pairwise) compared with the reduced (Fe²⁺) and oxidized (Fe³⁺) Hb WT. The average reduced (Fe²⁺) RMSF is larger than the oxidized (Fe³⁺) state for both these variants (Tables S2 and S3). This is in contrast to the WT and other Hb variants, suggesting that the reduced state fluctuations are higher in these variants. Recently, a crystal structure (PDB: 3QJD) for the Kirklareli variant has been reported (67). The pairwise C α atom RMSD between the PDB: 1HGA and 3QJD is 1.00 Å, suggesting that the mutant adopts a similar globin structure (see Fig. S3). MD simulations starting from this structure showed similar trends in RMSF. Nonetheless, the Fe²⁺ state showed larger fluctuations for polar residues Asn78, His89, and Lys90. This suggests that the His58 interactions with heme stabilize the movement of proximal residues and mutation to a nonpolar leucine, thus increasing the dynamics of these residues. The Fe³⁺ state, on the other hand, had higher RMSFs in the loop region (residues 114–117). In contrast, the Hb J-Buda variant with a semiconservative mutation (K61N) showed minor fluctuations in the heme interacting loop (residues 44–54), whereas relatively larger differences in fluctuations are observed in the region 115–120, which indicates weaker interactions with the β chain (especially in the oxidized state; see Fig. 3). Except for the K61E and H58L variants, the RMSF values are consistently higher for the oxidized (Fe³⁺) state. This can be understood by considering the reduction in the electrostatic repulsion between the Glu side chain and the heme group in the oxidized state. These findings suggest that mutation in one region of the Hb can have significant influence on the dynamics in distant regions (68,69).

Figure 3.

Residue-wise RMSFs for the protein backbone for the Hb variants in the oxidized (ferric) and reduced (ferrous) states during the 40 ns MD simulations. The Hb Miyagi (K61E) and Hb Kirklareli variants form Hb M, whereas the Hb J-Buda (K61N) variant functions normally. To see this figure in color, go online.

A comparison of the RMSD between the Hb redox states for individual variants similarly shows that the variants leading to Hb M formation results in the largest movement in the protein backbone (see Figs. S4–S12).

Redox potentials and reorganization free energy for Hb WT, Hb mutants, and Cyt b5

The mutations studied in this work are within the Hb active site; additionally, previous and present docking models of the Hb-Cyt b5 complex estimate the Fe-Fe distance between the two heme cofactors to be >1 nm (or 10 Å) (70). Thus, it is reasonable to expect that the Hb mutations studied here primarily affect the redox properties of the Hb heme. Hence, we investigate whether there is a correlation between redox potentials and/or reorganization free energy for oxidation of Hb mutants and their propensity to form Hb M in experiments (Eq. 2).

$$\text{Reduced}Hb\left(R\right)\to \text{Oxidized }Hb\left(O\right)+e^{-}.$$ (2)

The redox potentials of Hb WT and mutants are obtained using the linear response approximation, E°_abs = (<ΔE>_R + <ΔE>_O)/(2e), where ΔE is the vertical energy gap, ΔE = E_O − E_R; E_O and E_R are the potential energies of the oxidized and reduced Hb (obtained from the AMBER force field energy (33)); <ΔE>_M, M = O, R, denotes the average vertical energy gap, obtained along MD trajectories run in oxidation state M; and e is the unit charge. In MD simulations in periodic boundary conditions, the absolute (abs) vertical energy gaps are not related to experimental observables because of the arbitrary zero of the Ewald potential, but their relative differences are physically meaningful. Therefore, we calculate the relative redox potentials of the Hb mutants with respect to WT, ΔE° = E°_abs(mutant) − E°_abs(WT), and add these shifts to the experimental redox potential of WT versus normal hydrogen electrode (NHE), E°(WT) = −0.165 V, to obtain our estimate for the redox potential of the mutants versus NHE, E°(mutant) = −0.165 V + ΔE°. The reorganization free energy for oxidation is typically divided into an inner- and outer-sphere part, λ = λ_is + λ_os. Previous calculations have shown that the inner-sphere contribution is very small for heme proteins (25 meV for a single bis-His coordinated heme) and is thus neglected (71), λ ∼λ_os. The outer-sphere contribution is obtained from the linear response approximations, λ_os = (<ΔE_os>_R − <ΔE_os>_O)/2. Because nonpolarizable force fields such as the one used here are known to systematically overestimate outer-sphere reorganization free energies, the latter were scaled down uniformly by a factor of 1.6, as recommended in (32).

The results of the calculations are summarized in Tables 1 and 2 (see also Tables S4 and S5). We first discuss the α analog of the Hb Zurich β variant in which a distal histidine is replaced by a noncoordinating arginine residue (H58R). We find a significant increase in redox potential from −0.165 to +0.064 V. The increase is in accord with expectations in the sense that when a neutral residue in the active site is mutated into a positively charged residue, the electron affinity of the cofactor increases. This indicates a lower equilibrium concentration of Hb M for this variant compared with WT. Although this variant has not been reported in the literature yet, its β analog, the Hb Zurich variant, has been found to be susceptible to oxidation (HbVar database). Our results suggest that this Hb (H58R) variant may not lead to a noticeable change in the background Hb M content. The situation is strikingly different for the Hb Miyagi variant. In this mutant, the active site residue Lys61 that forms a key H-bonding interaction with a heme carboxylate is mutated into a Glu residue. This results in a large predicted decrease of redox potential from −0.165 to −0.296 V. This is in accord with expectations, as the positively charged Lys is replaced by a negatively charged Glu. This suggests a higher equilibrium concentration of Hb M, in agreement with experimental observations (HbVar database). The Hb J-Buda variant involves a mutation of the same Lys61 to a semiconservative Asn residue. Going from a positively charged to a neutral residue, the decrease in redox potential is smaller, E° = −0.204 V. Finally, the Hb Kirklareli variant involves the substitution of His58 with a leucine. Our calculations predict a small decrease in the estimated E° by only ∼10 mV with regard to the WT. MD simulations starting from a more recently reported crystal structure for this variant (3QJD) (67) give a small increase in 15 mV with regard to the WT. Neither simulation clearly supports the experimental observation that Hb M content for this variant is markedly increased (HbVar database) (67).

Table 1.

Computed redox potentials versus NHE and reorganization free energies for Hb, selected α chain Hb variants, and Cyt b5

Protein	Mutation	λa (eV)	E°a (V)	Hb M formation
Hb	WT	0.69	−0.165b	<1%
α analog of the Hb Zurich β variant	H58R	0.72	−0.064	NAc
Hb Miyagi	K61E	0.73	−0.296	increased Hb M formation
Hb J-Buda	K61N	0.67	−0.204	NAc
Hb Kirklareli	H58L	0.70	−0.176	increased Hb M formation
Hb Kirklareli (3QJD)	H58L	0.69	−0.150
Cyt b5 (3NER)	wild	0.93	−0.212	not applicable

^aSee main text for details of calculations.

^bExperimental redox potential versus NHE for T-state Hb, from (20).

^cInformation not available in the HbVar database and literature.

Table 2.

Decomposition of outer-sphere reorganization free energy in protein and solvent contribution, all values in eV

Hb α chain variants	Mutation	λ	λprot	λsolv	% Contribution of λsolv to λ
Hb	WT	0.69	0.16	0.53	76
Hb M Boston	H58Y	0.69	0.17	0.52	75
α analog of the Hb Zurich β variant	H58R	0.72	0.18	0.54	75
Hb Miyagi	K61E	0.73	0.02	0.71	97
Hb J-Buda	K61N	0.67	0.03	0.64	95
Hb Kirklareli	H58L	0.70	0.19	0.51	73

Reorganization free energies of all mutants are very similar to the WT; the small changes among the mutants are insignificant in terms of ET rates, indicating that this parameter does not correlate with propensity for Hb M formation. The λ-value for the WT (0.69 eV) is lower than the value reported by Blankman et al. (21) for the Hb tetramer. It should be noted that this value for the Hb tetramer include λ contributions from the β subunit, which is known to undergo larger structural changes upon ligand binding, and hence, a slightly larger λ for the tetrameric complex is expected (Figs. 8 a and 10 of (43)).

We have also estimated the reorganization free energy for oxidation of Cyt b5, the protein that donates an electron to Hb. This parameter is needed later (Modeling the Cyt b5-Hb WT complex and Rates for ET between Cyt b5 and Hb α chain variants) for estimation of ET rates. Only one crystal structure for only one human Cyt b5 has been reported (PDB: 3NER) (56). Thus, this structure was used for the calculations. Protein preparation, heme parameterization, and MD simulations were performed using the protocol mentioned in the Materials and methods. The energy gaps for the Cyt b5 are considerably larger than those predicted for Hb and its variants (see Table S4). This is probably due to the smaller size and associated larger conformational change in the protein structure upon oxidation. The λ-value for Cyt b5 is also larger than for Hb, λ = 0.93 eV after scaling. This estimate is larger than the electrochemically determined value (λ = 0.44 eV (21)). This can be expected because the electrochemical adsorption and protein complexation significantly stabilize the protein dynamics in Cyt b5 in comparison with the isolated solution state. The redox potential of Cyt b5, −0.212 V from experiment, is more negative than for Hb WT, resulting in a driving force of −0.047 eV.

Contributions of protein and solvent to the reorganization energies

As mentioned earlier, the total reorganization energy (λ) comprises the inner-sphere and outer-sphere contributions. Similar to cytochromes, the relatively rigid nature of the heme cofactor causes the inner-sphere reorganization energies to be small for Hb and variants with mutations in the outer-sphere protein environment (72). Table 2 shows the scaled protein reorganization energies (λ_prot), calculated by stripping the solvent and ions from MD trajectories and re-estimating the AMBER energies with the ff19SB force field. The solvent reorganization energies (λ_solv) are then estimated as the difference between the total and protein reorganization energies (i.e., λ_solv = (λ − λ_prot)). For all the Hb variants, including the WT, the major contribution to total λ comes from the solvent reorganization (λ_solv: 0.514–0.706 eV, 73–97%). For the Hb WT, the solvent contributes 76%. Nonetheless, the λ_prot are non-negligible for the Hb WT (0.162 eV, 24%) and the Hb M Boston variant (0.179 eV, 25%). The H58L (Hb Kirklareli) variant showed a larger protein reorganization (λ_prot = 0.186 eV, 27%) and solvent reorganization (λ_solv = 0.514 eV, 73%) comparable with the Hb WT in response to oxidation.

The Boston and H58R variants show λ_solv, and λ_prot values similar to the Hb WT. In the Hb WT, the side chain of Lys61 forms an average of two H-bonding interactions with the bulk water and one H-bond with heme carboxylates (see Fig. 4). These H-bond interactions between residue 61 and heme are lost in the K61E Hb Miyagi variant. The glutamate residue in the K61E Hb variant now forms an average of 5.8 and 4.3 H-bonds with the bulk water molecules in the reduced (Fe²⁺) and oxidized (Fe³⁺) states, respectively. The repulsion between the glutamate and heme carboxylate leads to a significant reorganization of solvent structure (λ_solv = 0.706 eV, 97%) forced by increased H-bonding with the surrounding water molecules. The Lys61 residue of the WT Hb forms H-bonds with the heme in 26% of the frames and thus stabilizes the additional negative charge in the reduced (Fe²⁺) state (0.07% of the frames in oxidized, Fe³⁺ state). This reduces to negligible (0.0075% of the frames) in the K61N variant and zero in the K61E variant. This explains the unexpectedly lower protein reorganization in these variants in response to oxidation. This suggests that the Lys61 residue plays a key role in determining the protein reorganization in response to oxidation and mutation at this site (especially into a negatively charged amino acid) increases Hb M formation. The larger protein reorganization (λ_prot) in the Hb WT prevents faster oxidation to Hb M, but mutation of Lys to uncharged or negatively charged residues lowers the λ_prot, facilitating Hb M formation. Although there is a corresponding increase in the λ_solv, this is likely to be spread out among a large number of bulk water molecules, thus keeping the activation free energy lower than the Hb WT.

Figure 4.

Number of H-bonds formed between the side chain of the residue 61, solvent water, and heme carboxylate in the Hb WT (K61) and in the Hb M Miyagi variant (K61E) during the 40 ns MD simulation. To see this figure in color, go online.

The Hb J-Buda variant, which involves a semiconservative mutation (K61N), forms an average of only 1.1 H-bond interactions with the bulk water (data not shown) and no interactions with the heme group. This explains the lowest average RMSF calculated for both the K61E and K61N variants (Table S3). Nonetheless, there is a difference of 0.068 eV in λ_solv between these two variants, with the K61N (Hb J-Buda) being similar to the Hb WT. This, coupled with the larger oxidation free energy difference (0.13 eV) for the Hb Miyagi (K61E) variant, also offers logical explanation for its lower redox potential.

Modeling the Cyt b5-Hb WT complex

Since the early docking and Brownian dynamics attempts to model the Cyt b5-Hb complex, the explicit modeling of the complex and ET parameters for the reduction of Hb by Cyt b5 have not received much attention (23,26,29). Although the docking-based models serve as the starting point in the absence of complex crystal structures, some features, such as the heme edge-to-edge distances predicted by these models, have been questioned earlier (24). Thus, protein-protein docking between Cyt b5 and Hb was followed by all-atom explicit MD simulations to address these aspects. The bis-His heme of Cyt b5 was parameterized using the MCBP.py tool and a procedure similar to that given in Heme parameterization with MCBP.py and quantum chemical calculations.

MD simulations for 40 ns in each of the redox states, namely Hb (Fe³⁺)-Cyt b5(Fe²⁺) and Hb (Fe²⁺)-Cyt b5 (Fe³⁺), were performed. The docked complex with Cyt b5 in the reduced (R) and Hb in the oxidized (O) state showed Fe-Fe and minimal heme edge-to-edge distances of 16.9 and 4.5 Å, respectively (see Fig. 5). The heme groups gradually move away from each other during the MD simulation, giving average values of 23.506 and 12.119 Å for the Fe-Fe and heme edge-to-edge distances, respectively. An analysis of the intermolecular H-bonding interactions between the two proteins during the MD (Tables S6 and S7) showed that Hb residues His89, Lys90, Arg92, and Arg141 are the major H-bond donors, whereas Cyt b5 residues Glu191, Glu195, Gly209, Asp207, and heme carboxylates are the major H-bond acceptors. On the other hand, the Cyt b5 residues act as H-bond donor and Hb residues as H-bond acceptor only rarely (<10%). The analysis of native contacts between the two protein chains (Table S8) shows a similar interaction profile. These complementary interactions observed during MD simulations are different from those estimated from protein-protein docking simulations. This suggests that the protein complex is considerably dynamic and does not bind in one particularly stable conformation but samples different configurations. These observations are in agreement with the dynamic docking hypothesis (23).

Using the Marcus formalism and linear response approximation, the ET between the two proteins can be modeled as shown in Eqs. 3, 4, and 5.

$$Cytb{5}_{Red}+H{b}_{oxd}\left(RO\right)\to Cytb{5}_{oxd}+H{b}_{Red}\left(OR\right).$$ (3)

The barrier for the ET can be estimated using Eq. 4.

$$\Delta G^{‡}=\left(\frac{{\left(\lambda +\Delta G^o\right)}^2}{4\lambda }\right).$$ (4)

The ET rate can then be predicted using the semiclassical Marcus theory and associated Eq. 5, where H_ab is the electronic coupling between the two heme cofactors, ħ is the modified Plank’s constant, k_B is the Boltzmann constant, and T = 300 K. ET parameters for the complex are shown in Table 3.

$$k_{ET}=\frac{2\pi }{\hslash }\times {\left|H_{ab}\right|}^2\times {\left(4\pi \lambda k_{B}T\right)}^{-1/2}\times e^{\left(\frac{-{\left(\lambda +\text{Δ}G°\right)}^2}{4\lambda k_{B}T}\right)}.$$ (5)

Table 3.

Parameters and rates for ET from Cyt b5 to Hb M WT and variants

Protein	Mutation	ΔG° (eV)	λ (eV)	ΔG‡ (eV)	kET (s−1)
Hb	WT	−0.047a	1.384	0.323	185.8 (experiment 120) (24)
α analog of the Hb Zurich β variant	H58R	−0.148	1.420	0.285	797.7
Hb Miyagi	K61E	0.084	1.428	0.401	9.1
Hb J-Buda	K61N	−0.008	1.368	0.338	104.9
Hb Kirklareli (3QJD)	H58L	−0.047	1.385	0.323	242.5

^aExperimental driving force for ET from Cyt b5 to Hb.

The electronic coupling (H_ab) can be estimated from its empirical distance dependence relationship (Fig. 2 of (73)). Thus, H_ab = A × exp[−β × (R − R₀)/2], where the pre-exponential factor is 0.022 eV, β = 1.39 Å⁻¹, R₀ = 3.6, and R is the heme edge-to-edge distance between the proteins. Using the average of the minimal heme edge-to-edge distance (12.1 Å) from the MD simulation gives a small coupling energy, H_ab = 5.9 × 10⁻⁵ eV. The reorganization free energy for ET is estimated as the sum of the reorganization free energy of the isolated proteins (corresponding to ET at infinite ET distance), and the effect of finite ET distance (12.1 Å) was accounted for using the Marcus continuum formula for outer-sphere reorganization. All ET parameters are summarized in Table 3. This gives an estimate of k_ET = 185.8 s⁻¹ for the ET, in close agreement with the ∼120 s⁻¹ reported by Qiao et al. (24) for the reaction at 25°C. Our predictions are also higher than the electrochemical rate measurements (k_ET = 0.037 s⁻¹) reported by Blankman et al. (21), who used the work term and electrostatics corrections on the predictions from Marcus and Sutin’s relationship between ET kinetics and electrode half reactions (74). This disagreement between electrochemical and solution ET values is expected because ET at the electrodes is known to be usually slower than in native protein complexes. Using Eq. 4, the ET barrier (ΔG^‡) for the WT complex was calculated to be 0.323 eV. Considering the experimental uncertainty of ∼0.1 eV (2.3 kcal/mol), this can be considered as a reasonable agreement with the experimental value of 4 kcal/mol value reported by Simons et al. (24). Thus, we use the same procedure to calculate the ET rates from Cyt b5 to Hb variants in the next section.

Rates for ET between Cyt b5 and Hb α chain variants

To assess the influence of mutation, we focused on the prediction of relative changes in the ET rates (k_ET) and barriers (ΔG^‡) for the reduction of Hb variants using Marcus ET parameters calculated in Redox potentials and reorganization free energy for Hb WT, Hb mutants, and Cyt b5. Because these variants involve single point mutations of residues within the Hb active site with close interactions with heme, it is reasonable to assume that they have little impact on the protein-protein interactions in Cyt b5 and Hb complexes, and thus, the electronic coupling (H_ab = 5.9 × 10⁻⁵ eV) remains small. Thus, the ET λ for the Hb variants can be considered equal to the sum of the ET λ for the WT complex and difference of oxidation λ between the mutant and the Hb WT α chain (Table 3). Thus, for example, using values in Tables 1 and 3, the ET λ for the H58R Hb variant complex with Cyt b5 is 1.420 = (1.384 + (0.721 − 0.6853). The ET free energy change (ΔG°) is equal to the difference in the redox potentials (ΔE°) between the Cyt b5 and the Hb variant.

Thus, ET barriers (ΔG^‡) and rates (k_ET) for Cyt b5-Hb variant complexes can be calculated using Eqs. 4 and 5, respectively, and are shown in Table 3. Our predictions for the ET rate suggest that the Hb M of the H58R variant will be reduced faster upon oxidization to Hb M. The ET rate for the Hb Miyagi variant is lowest at 9.1 s⁻¹. Hence, this variant features not only the highest equilibrium concentration of Hb M but also the slowest Hb M reduction rates. ET rate and ΔG^‡ calculations for the J-Buda variant suggest that this variant will be reduced more slowly than the Hb WT. Additionally, the lower E° predicted for this variant also suggests that the equilibrium concentration of Hb M for the J-Buda variant might be higher than the Hb WT. Thus, the presence of this variant should be assessed carefully in the patient groups at higher risk of oxidative stress.

For the Hb Kirklareli variant, the ET rate (k_ET = 242.5 and 130.9 s⁻¹) calculated using the PDB: 3QJD and 1HGA structures, respectively, gives an average similar to the Hb WT. The ET barrier (ΔG^‡) is also calculated to be similar to the WT. Nonetheless, the lower E° estimated for this variant suggests a higher equilibrium Hb M concentration that is in agreement with in vitro experimental findings and clinical reports.

Conclusions

In summary, the answer to the questions asked in the introduction are as follows. 1) The single point mutations studied here mostly do not disrupt the globin structure. Major exceptions to this are the His → Tyr mutations (Hb M Boston, distal site and Hb M Iwate, proximal). In the latter variant, a heme transfer to Tyr is reported in the literature. Mutants K61E, K61N, H58R, and H58L show influence on the selected regions of the globin chain (loop 44–54 and region 114–120). 2) All-atom MD simulations and average vertical energy gap calculations allow reasonably accurate prediction of Marcus parameters (λ and ΔG°) that are in agreement with literature reports on similar heme proteins. 3) All the Hb M-forming mutations (H58Y, K61E, and H58L) lead to a marginal increase in the total reorganization energy (λ) associated with the Hb oxidation, whereas the Hb J-Buda (K61N) shows a small decrease in λ. The calculated redox potentials are in correspondence with the known propensity of these variants to form Hb M. 4) The solvent reorganization (λ_solv) makes the largest contributions for all the variants (including the Hb WT). The mutation of the Lys residue has the largest influence on the protein reorganization energies (λ_prot), thus highlighting its role in the stabilization of the reduced (Fe²⁺) state and normal Hb structure and function. 5) The calculated Marcus ET parameter, redox potentials, offers an explanation for the corresponding higher and moderate propensity of Hb oxidation to Hb M for the K61E and K61N mutants, respectively. Our calculations are also consistent with the reports that H58L variant (Hb Kirklareli) undergoes faster autoxidation (lower E° than Hb WT). 6) Calculations of the ET parameters and reduction rate predictions using MD simulations for the Cyt b5-Hb complex and semiclassical Marcus ET theory are in close agreement with experimental measurements. Additionally, the reduction rate prediction of Hb variants is also in agreement with available in vitro rate data and clinical observations of Hb M formation. Thus, a combination of thermodynamic (E°) and kinetic (ΔG^‡, k_ET) considerations allows us to rationalize the formation of Hb M in the Miyagi and Kirklareli variants and lack thereof in the Hb WT and J-Buda.

Finally, this study represents the first attempt, to calculate Marcus parameters for the oxidation of Hb and reduction rates of Hb M using all-atom MD simulations of the redox states. Our graphics processing unit (GPU) enabled MD simulations, postprocessing, calculations, and data analysis completed within 4–5 h per mutant. Thus, this methodology can be applied to other Hb variants and heme proteins to extract meaningful predictions and may have a potential to guide experimental studies on most medically relevant and industrially useful mutations.

Author contributions

V.A.D. conceptualized the project, wrote funding proposal, performed literature search and calculations, analyzed results, wrote the manuscript, and participated in discussions. J.B. analyzed the results, provided expert opinion, and participated in manuscript writing and discussions. S.K.V. performed preliminary literature and database search and participated in discussions.

Editor: Alan Grossfield.

Supporting citations

References (75, 76, 77, 78, 79, 80, 81, 82) can be found in the Supporting material.